Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #440 |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,131|a^2=e,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^1301322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #440×D131, C2×#22553410, #30674759, … |
| maximal normal subgroup of | #440×D131, C2×#22553410, #30674759, … |
| maximal quotient of | #30664771, #30664816, #30664839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 647);